Solve this real-world problem using a system of equations. The O’Donnells are having a birthday party for their son, and they plan to have a clown bring balloons to the party. Balloon Express charges $2 per balloon and $10 for delivery. Balloon Mania charges $1.50 per balloon and $20 for delivery. If the O’Donnells plan to order 30 balloons, which company should they choose, and how much will they save?(1 point) Responses Balloon Express; $5 Balloon Express; $5 Balloon Express; $25 Balloon Express; $25 Balloon Mania; $25 Balloon Mania; $25 Balloon Mania; $5 Balloon Mania; $5

1 answer

To determine which balloon company is the better choice for the O'Donnells, we can set up a system of equations to calculate the total cost for each company based on the number of balloons ordered.

Let \( x \) be the number of balloons ordered, which is 30.

For Balloon Express:

  • Cost per balloon: $2
  • Delivery fee: $10

The total cost for Balloon Express can be calculated as follows: \[ \text{Total Cost}{\text{Express}} = 2x + 10 \] Substituting \( x = 30 \): \[ \text{Total Cost}{\text{Express}} = 2(30) + 10 = 60 + 10 = 70 \]

For Balloon Mania:

  • Cost per balloon: $1.50
  • Delivery fee: $20

The total cost for Balloon Mania can be calculated as follows: \[ \text{Total Cost}{\text{Mania}} = 1.5x + 20 \] Substituting \( x = 30 \): \[ \text{Total Cost}{\text{Mania}} = 1.5(30) + 20 = 45 + 20 = 65 \]

Now we can compare the total costs:

  • Total cost for Balloon Express: $70
  • Total cost for Balloon Mania: $65

To find out how much the O'Donnells will save by choosing Balloon Mania over Balloon Express: \[ \text{Savings} = \text{Total Cost}{\text{Express}} - \text{Total Cost}{\text{Mania}} = 70 - 65 = 5 \]

Thus, the O'Donnells should choose Balloon Mania and they will save $5.

The answer is: Balloon Mania; $5